Inferring global exponents in subsampled neural systems

In systems exhibiting avalanche-like activity, critical exponents can provide insights into the mechanisms un- derlying the observed behavior or on the topology of the connections. However, when only a small fraction of the units composing the system are observed and sampled, the measured exponents may differ significantly from the true ones. In this study, using branching process and (2 + 1)D directed percolation, we show that some of the exponents, namely the ones governing the power spectrum and the detrended fluctuation anal- ysis (DFA) of the system activity, are more robust and are unaffected in some intervals of frequencies by the subsampling. This robustness derives from the preservation of long-time correlations in the subsampled signal, even though large avalanches can be fragmented into smaller ones. These results don’t depend on the specific model and may be used therefore to extract in a simple and unbiased way some of the exponents of the unobserved full system.